Simplify sin(x)^2+cot(x)cos(x)sin(x)

$\sin^{2} (x) + \cot (x) \cos (x) \sin (x)$

Step 1

Simplify each term.

Rewrite $\cot (x)$ in terms of sines and cosines.

$\sin^{2} (x) + \frac{\cos (x)}{\sin (x)} \cos (x) \sin (x)$

Multiply $\frac{\cos (x)}{\sin (x)} \cos (x)$ .

Combine $\frac{\cos (x)}{\sin (x)}$ and $\cos (x)$ .

$\sin^{2} (x) + \frac{\cos (x) \cos (x)}{\sin (x)} \sin (x)$

Raise $\cos (x)$ to the power of $1$ .

$\sin^{2} (x) + \frac{\cos^{1} (x) \cos (x)}{\sin (x)} \sin (x)$

Raise $\cos (x)$ to the power of $1$ .

$\sin^{2} (x) + \frac{\cos^{1} (x) \cos^{1} (x)}{\sin (x)} \sin (x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin^{2} (x) + \frac{{\cos (x)}^{1 + 1}}{\sin (x)} \sin (x)$

Add $1$ and $1$ .

$\sin^{2} (x) + \frac{\cos^{2} (x)}{\sin (x)} \sin (x)$

Cancel the common factor of $\sin (x)$ .

Cancel the common factor.

$\sin^{2} (x) + \frac{\cos^{2} (x)}{\sin (x)} \sin (x)$

Rewrite the expression.

$\sin^{2} (x) + \cos^{2} (x)$

Step 2

Apply pythagorean identity.

$1$